How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, to differentiate a function of a function of x, we first differentiate the 'outside' function while leaving the 'inside' function unchanged; then we differentiate the 'inside' function; then we multiply the two together. In this case, the inside function (g) is the e^(2x)+1 and the outside function (f) is the 'cubed'. Therefore, f'(g(x)) = 3(e^(2x)+1)^2, and g'(x) = 2(e^(2x)). So:(d/dx)((e^(2x)+1)^3) = (3(e^(2x)+1)^2) * 2(e^(2x)) = 6((e^(2x)+1)^2)(e^(2x))